Low Back and Common Widespread Pain Share Common Genetic Determinants

doi: 10.1111/ahg.12074

Low Back and Common Widespread Pain Share Common Genetic Determinants Ida Malkin1 , Frances M. K. Williams2 , Genevieve LaChance2 , Timothy Spector2 , Alex J. MacGregor2,3 and Gregory Livshits1,2∗ 1 Department of Anatomy and Anthropology, Sackler Faculty of Medicine, Tel Aviv University, Israel 2 Department of Twin Research and Genetic Epidemiology, King’s College London, UK 3 School of Medicine, University of East Anglia, Norwich, UK

Summary Low back (LBP) and chronic widespread musculoskeletal pain (CWP) both have a significant genetic component and are associated with increased body mass index (BMI). We examined whether LBP and CWP share common genetic factors, and to what extent this correlation is modified by the genetic factors influencing BMI. Genetic analysis of binary traits such as pain is not simple, particularly if their risk is associated with age or other quantitative traits. Implementing Falconer’s polygenic threshold concept for dichotomous traits inheritance, we developed new software to examine the extent of the genetic influence on LBP and CWP under age and BMI dependence. The analysis was conducted on 3266 and 2256 UK female twins, assessed for LBP and CWP, respectively. Analysis of the liability scores with threshold to LBP and CWP established substantial contribution of genetic factors to their variation (h2 > 0.60, p τ ). Assuming each individual in the sample has some covariate measurements Yn , the probability density of individual liability can be presented as a normal distribution around the predicted value F(Yn ). The multiple regression coefficients for covariates in F(Y) are determined in maximum likelihood estimates (MLE). Following Falconer (1965), we assumed in our analysis a multifactorial, polygenic nature of the liability scores. This allows implementation of a variance component analysis (VCA), assuming that variation in liability scores is caused by orthogonal (independent) variance components, namely, VX = VAD + VCE +V RS , where VAD , VCE , VRS are variance components reflecting additive genetic, common family, and random environment effects, respectively (Falconer & Mackay, 1996). Consider a pedigree including N individuals. Each individual has a unique predicted value of liability F(Yn ). The probability density of joint pedigree liability residuals can be expressed as N-variable normal distribution with nonzero correlation between the relatives. The probability of the dichotomous trait values set {Bn } (affection status) observed in the pedigree members is computed as an N-dimensional threshold integral of the joint probability density through each individual variable Xn , from - to τ (if Bn = 0), or from τ to + (if Bn = 1). The computation of this integral is an immense task, and therefore here we propose a new formulation of joint VC likelihood, which makes this computation easier (see Appendix). We propose modified quasi VCA (QVCA) joint likelihood expression to fit the liability transmission and a QVCA maximization procedure estimating the variance of components (VAD , VCE , VRS ) and the affection threshold τ on a liability scale. A major strength of this approach is that our software allows the explicit inclusion of covariates in the model and estimates proportion of liability variance attributable to covariates. The procedure is written on C++ and included in the new version of MAN package for pedigree analysis (Malkin & Ginsburg, 2014).

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2014 John Wiley & Sons Ltd/University College London

Genetics of LBP and CWP

Table 1 Basic descriptive statistics of the study sample by affection status. LBP = 0 (1710)

LBP = 1 (546)

Trait

Mean

SD

Mean

SD

Age [years] Height [m] Weight [kg] BMI [kg/m2 ]

49.95 1.62 64.89 24.69

11.78 0.06 11.32 4.29

51.48 1.63 68.97 25.92

10.28 0.06 12.93 4.79

CWP = 0 (2585)

CWP = 1 (681)

t-testa

Mean

SD

Mean

SD

t-testa

2.92 3.39 6.60 5.35

53.27 1.62 66.41 24.48

14.21 0.06 12.03 4.30

58.77 1.61 70.95 26.37

10.94 0.06 14.40 5.20

10.91 4.60 7.57 8.75

a t-tests compare the corresponding variable between the affected (1) and unaffected (0) individuals, for each pain phenotype separately, all tests have P < 0.05.

Table 2 Affected vs unaffected CWP and LBP individuals in study sample (2×2 contingency table). The sample shows statistically highly significant dependence (coincidence) between the two pain phenotypes χ 2 = 107.4, P < 0.0001. ∗

CWP =1 LBP\CWP LBP = 1 LBP = 0 Total

Expected 72.6 243.4 316

CWP = 0 Observed 140 176 316

Expected 225.4 755.6 981

Observed

Total

158 823 981

298 999 1297

∗

1 and 0 represent affected and unaffected individuals correspondingly.

Using the likelihood ratio test (LRT) as a model-fitting technique, a best fitting and most parsimonious model was obtained for the pattern of inheritance of CWP, LBP, and BMI. Since significant associations were observed between the study phenotypes, we examined to what extent these associations could be attributed to shared genetic or environmental factors. To test this hypothesis, we used bivariate QVCA, which assumes that observed phenotypic correlations can be caused by pleiotropic genetic factors (as measured by additive genetic correlation), and/or by shared environmental factors (measured by environmental correlation) (Falconer & Mackay, 1996).

Results Table 1 provides the basic descriptive statistics of the study sample. Since LBP and CWP were assessed in TwinsUK at different time-points and were not fully overlapping (1297 individuals had completed both pain questionnaires) the corresponding anthropometric and demographic information is given separately. Cases of both pain phenotypes showed the same trend compared to controls: they were on average older and heavier in body weight. The χ 2 test for the independence of these two phenotypes (Table 2) rejected the null hypoth-

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2014 John Wiley & Sons Ltd/University College London

esis of no association (P < 0.0001). Next using the binary logistic regression, we examined whether the probability of an individual having LBP or CWP was associated with increased BMI, independently of age. In both cases, the results were statistically significant with odds ratios (OR) per SD of BMI change: 1.325 (1.200–1.462, p = 2.3E-8) and 1.357 (1.225–1.503, p = 4.6E-09). We then examined the contribution of common and trait specific genetic and environmental factors to inter-individual variability and co-variability of liability score and LBP, CWP, as well as BMI. Tetrachoric correlations for MZ vs DZ twins by phenotype were: 0.733 vs 0.422 for CWP, 0.634 vs 0.363 for LBP, and 0.526 vs 0.179 for cross-phenotype associations, and were statistically significant: P = 0.015 for DZ twins cross-phenotype associations, and P < 0.001 for all others. These estimates provide evidence of the familial, likely genetic, factors contributing to the risk of chronic pain. This was confirmed in a univariate modeling of CWP and LBP variations (Table 3). In particular, this shows that the contribution of common twin environment was negligible (P > 0.20), while contribution of the putative genetic factors was quite substantial (h2 > 0.60) and by LRT statistically highly significant with p = 4.2E-03 and 2.6E-04 for LBP and CWP, respectively. The threshold for the corresponding liability scores for LBP and CWP was estimated at 0.72 SD and 0.84 SD, respectively. The bivariate model also showed a highly significant association between LBP and CWP caused both by shared genetic and shared environmental factors, resulting in significant genetic (RAD ) and environmental (RRS ) correlations (Table 4). Parameters ν AD [1], ν AD [2] determine for each trait the proportion of additive genetic variance attributed to genetic factor, which influences both traits simultaneously; ν RS [1], ν RS [2] estimate the same proportions for individual environmental variance (see Appendix). These parameters indicate that 39% for CWP to 70% for LBP of the trait heritability is attributable to shared genetic effects, and roughly 40% and 67% of the residual variation is caused by the environmental factors simultaneously affecting both pain syndromes.

Annals of Human Genetics (2014) 00,1–10

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I. Malkin et al.

Table 3 Best fitting and most parsimonious models for BMI and for liability scores to LBP and CWP. Parametera

BMI

LBP

CWP

VAD VSB VRS a0 b1 [Age_s] b2 [(Age_s)2 ] τ V_age P{LRT(VAD =0)}

0.710 ± 0.043 [ 0 ]b {0.261}c 0.099 ± 0.020 0.166 ± 0.016 −0.036 ± 0.013

0.624 ± 0.218 [0] {0.362} {0.044} 0.098 ± 0.043 −0.079 ± 0.038 0.716 ± 0.035 0.014 4.2E-03

0.636 ± 0.174 [0] {0.257} {0.141} 0.215 ± 0.035 −0.129 ± 0.027 0.839 ± 0.030 0.107 2.6E-04

0.029